Two isolated, concentric, conducting spherical shells have radii R and 2R and uniform charges q and 2q respectively. If `V_1` and `V_2` are potentials at points located at distances 3R and `R/2` , respectively, from the centre of shells. Then the ratio of `(V_2/V_1)` will be

Options

A. 2
B. 1
C. `1/2`
D. 0

Answer

A

Explanation

For point, ` r = R/2`
` V_1` = Potential of surface radius R+ Potential of surface radius 2R
` = (kq)/(R) + (k2q)/(2R) = (2kq)/(R)`
For point r = 3R ,
` V_2` = Potential due to charges q and 2q assumed to be concentrated at centre ` = (k(3q))/(3R) = (kq)/(R)`
so ratio `V_1/V_2 = 2`